Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1112 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #20288856 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20284067 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #20284062 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20276737 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #20276736 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20276734 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #20276733 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #20276731 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #20276399 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #20276397 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C53×#2203 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #16811460 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | #16811422 | — | 2 | 2 | no | — |
| 14 | #16811419 | — | 2 | 1 | no | — |
| 15 | #16811372 | C22 | 1 | 2 | yes | complemented |
| 16 | #16811371 | — | 2 | 1 | no | — |
| 17 | #16811369 | — | 2 | 2 | no | — |
| 18 | #16811365 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #16811364 | — | 2 | 2 | no | — |
| 20 | #16811363 | — | 2 | 1 | no | — |
| 21 | #16811174 | C22 | 1 | 2 | yes | — |
| 22 | #16811172 | C22 | 1 | 1 | yes | characteristic |
| 23 | #16811158 | — | 2 | 1 | no | — |
| 24 | #16811156 | — | 2 | 2 | no | — |
| 25 | #16811136 | — | 2 | 2 | no | — |
| 26 | #16811131 | — | 2 | 1 | no | — |
| 27 | #16810808 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #16810806 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #16810805 | C22 | 1 | 2 | yes | complemented |
| 30 | #16810802 | — | 2 | 1 | no | — |
| 31 | #16810799 | — | 2 | 2 | no | — |
| 32 | #16810798 | C22 | 1 | 2 | yes | — |
| 33 | #16810796 | C22 | 1 | 2 | yes | — |
| 34 | #16810795 | C22 | 1 | 1 | yes | characteristic |
| 35 | #16810792 | — | 2 | 2 | no | — |
| 36 | #16810789 | — | 2 | 1 | no | — |
| 37 | #104×D53 | — | 2 | 1 | no | — |
| 38 | #104×D53 | — | 2 | 2 | no | — |
| 39 | #16810606 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | #16810606 | C22 | 1 | 2 | yes | complemented |
| 41 | #16810422 | C22 | 1 | 2 | yes | complemented |
| 42 | #16810421 | C22 | 1 | 2 | yes | complemented |
| 43 | #16810420 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | #16810419 | C22 | 1 | 2 | yes | complemented |
| 45 | #16810419 | C22 | 1 | 2 | yes | complemented |
| 46 | C53×#563 | C22 | 1 | 1 | yes | characteristic, complemented |
| 47 | C53×#456 | C22 | 1 | 2 | yes | complemented |
| 48 | C53×#454 | C22 | 1 | 1 | yes | characteristic |
| 49 | C53×#356 | C22 | 1 | 2 | yes | complemented |
| 50 | C53×#355 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | #13133265 | — | 4 | 1 | no | — |
| 52 | #13133265 | C23 | 1 | 1 | yes | characteristic |
| 53 | #13133263 | — | 2 | 1 | no | — |
| 54 | #13133263 | — | 2 | 2 | no | — |
| 55 | #13133263 | — | 4 | 1 | no | — |
| 56 | C2×#11719949 | — | 4 | 1 | no | — |
| 57 | C2×#11719949 | D4 | 1 | 2 | yes | — |
| 58 | C2×#11719949 | C23 | 1 | 1 | yes | characteristic |
| 59 | C2×#11719947 | D4 | 1 | 1 | yes | characteristic |
| 60 | #41×D53 | — | 2 | 1 | no | — |
| 61 | #41×D53 | — | 2 | 2 | no | — |
| 62 | #41×D53 | — | 4 | 1 | no | — |
| 63 | C22×C4×D53 | — | 2 | 1 | no | — |
| 64 | #13133250 | — | 2 | 1 | no | — |
| 65 | #13133249 | — | 4 | 2 | no | — |
| 66 | #13133248 | — | 2 | 2 | no | — |
| 67 | #13133247 | — | 2 | 1 | no | — |
| 68 | #13133246 | — | 4 | 1 | no | — |
| 69 | #13133245 | — | 2 | 2 | no | — |
| 70 | #13133244 | — | 4 | 2 | no | — |
| 71 | #13133243 | — | 2 | 1 | no | — |
| 72 | #13133242 | — | 2 | 2 | no | — |
| 73 | #13133241 | — | 4 | 1 | no | — |
| 74 | #13133240 | — | 4 | 2 | no | — |
| 75 | #13133238 | — | 4 | 2 | no | — |
| 76 | #13133238 | — | 4 | 1 | no | — |
| 77 | #13133236 | — | 4 | 1 | no | — |
| 78 | M16×D53 | — | 2 | 1 | no | — |
| 79 | M16×D53 | — | 2 | 2 | no | — |
| 80 | #13133215 | C23 | 1 | 1 | yes | characteristic |
| 81 | #13133214 | D4 | 1 | 2 | yes | — |
| 82 | #13133213 | D4 | 1 | 1 | yes | characteristic |
| 83 | #13133212 | — | 2 | 2 | no | — |
| 84 | #13133211 | — | 2 | 2 | no | — |
| 85 | #13133207 | — | 2 | 2 | no | — |
| 86 | #13133206 | D4 | 1 | 2 | yes | — |
| 87 | #13133206 | C23 | 1 | 2 | yes | — |
| 88 | #13133205 | — | 2 | 1 | no | — |
| 89 | #13133205 | D4 | 1 | 1 | yes | characteristic |
| 90 | #13133203 | — | 2 | 2 | no | — |
| 91 | #13133202 | — | 2 | 2 | no | — |
| 92 | #13133202 | — | 2 | 2 | no | — |
| 93 | #13133202 | — | 2 | 2 | no | — |
| 94 | #13133202 | — | 2 | 2 | no | — |
| 95 | #13133200 | — | 2 | 1 | no | — |
| 96 | #13133199 | — | 2 | 2 | no | — |
| 97 | #13133197 | — | 2 | 1 | no | — |
| 98 | #13133195 | — | 2 | 2 | no | — |
| 99 | #13133195 | — | 2 | 2 | no | — |
| 100 | #13133193 | — | 2 | 2 | no | — |
| 101 | #13133192 | — | 2 | 1 | no | — |
| 102 | #13133192 | — | 2 | 2 | no | — |
| 103 | #13133192 | — | 2 | 2 | no | — |
| 104 | #13133192 | — | 2 | 2 | no | — |
| 105 | #13133191 | — | 2 | 2 | no | — |
| 106 | #13133190 | — | 2 | 2 | no | — |
| 107 | #13133190 | — | 2 | 2 | no | — |
| 108 | #13133190 | — | 2 | 2 | no | — |
| 109 | #13133187 | — | 2 | 2 | no | — |
| 110 | #13133187 | — | 2 | 1 | no | — |
| 111 | #13133187 | — | 2 | 2 | no | — |
| 112 | #13133185 | — | 2 | 1 | no | — |
| 113 | #13133182 | — | 2 | 1 | no | — |
| 114 | #13133179 | — | 2 | 1 | no | — |
| 115 | #13133179 | — | 2 | 2 | no | — |
| 116 | #13133179 | — | 2 | 2 | no | — |
| 117 | #13133177 | — | 2 | 2 | no | — |
| 118 | #13133177 | — | 2 | 2 | no | — |
| 119 | #13133175 | — | 2 | 2 | no | — |
| 120 | #13133173 | — | 2 | 1 | no | — |
| 121 | C42×D53 | D4 | 1 | 2 | yes | — |
| 122 | C42×D53 | D4 | 1 | 1 | yes | characteristic |
| 123 | #13133145 | — | 2 | 2 | no | — |
| 124 | #13133145 | — | 2 | 1 | no | — |
| 125 | #13133144 | — | 2 | 1 | no | — |
| 126 | #13133144 | — | 2 | 2 | no | — |
| 127 | #13133143 | — | 2 | 1 | no | — |
| 128 | #13133143 | — | 2 | 2 | no | — |
| 129 | #13133136 | C23 | 1 | 1 | yes | characteristic |
| 130 | #13133136 | C23 | 1 | 2 | yes | — |
| 131 | #13133133 | — | 2 | 1 | no | — |
| 132 | #13133133 | — | 2 | 2 | no | — |
| 133 | 2−1+4×C53 | C23 | 1 | 1 | yes | characteristic |
| 134 | #137×C53 | — | 2 | 2 | no | — |
| 135 | AGL(1,ℤ/8)×C53 | — | 2 | 1 | no | — |
| 136 | C4⋊Q8×C53 | C23 | 1 | 2 | yes | — |
| 137 | #126×C53 | — | 2 | 2 | no | — |
| 138 | #125×C53 | — | 2 | 1 | no | — |
| 139 | #124×C53 | C23 | 1 | 1 | yes | characteristic |
| 140 | #123×C53 | — | 2 | 1 | no | — |
| 141 | C22⋊Q8×C53 | — | 2 | 2 | no | — |
| 142 | #104×C53 | — | 2 | 2 | no | — |
| 143 | #104×C53 | — | 2 | 1 | no | — |
| 144 | #101×C53 | C23 | 1 | 2 | yes | — |
| 145 | #101×C53 | C23 | 1 | 1 | yes | characteristic |
| 146 | C23×D53 | — | 2 | 1 | no | — |
| 147 | #41×C53 | — | 2 | 1 | no | — |
| 148 | #41×C53 | — | 2 | 2 | no | — |
| 149 | #41×C53 | — | 4 | 1 | no | — |
| 150 | C2×Q8×C53 | — | 4 | 1 | no | — |
| 151 | C2×Q8×C53 | C2×D4 | 1 | 2 | yes | — |
| 152 | C2×Q8×C53 | C24 | 1 | 1 | yes | characteristic |
| 153 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C22×C4×C53 | — | 2 | 1 | no | — |
| 155 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 156 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 157 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 158 | C22×Dic53 | — | 2 | 1 | no | — |
| 159 | #11719949 | — | 2 | 1 | no | — |
| 160 | #11719949 | — | 2 | 2 | no | — |
| 161 | #11719949 | — | 4 | 1 | no | — |
| 162 | #11719949 | — | 4 | 1 | no | — |
| 163 | #11719949 | — | 4 | 2 | no | — |
| 164 | #11719949 | — | 4 | 2 | no | — |
| 165 | #11719949 | — | 4 | 1 | no | — |
| 166 | #11719949 | — | 4 | 2 | no | — |
| 167 | #11719949 | — | 4 | 1 | no | — |
| 168 | Q8×D53 | — | 2 | 1 | no | — |
| 169 | Q8×D53 | — | 2 | 2 | no | — |
| 170 | Q8×D53 | — | 4 | 1 | no | — |
| 171 | #11719947 | — | 2 | 1 | no | — |
| 172 | #11719947 | — | 2 | 2 | no | — |
| 173 | #11719947 | — | 4 | 1 | no | — |
| 174 | #11719947 | — | 4 | 1 | no | — |
| 175 | #11719947 | — | 4 | 1 | no | — |
| 176 | D4×D53 | — | 2 | 1 | no | — |
| 177 | D4×D53 | — | 2 | 2 | no | — |
| 178 | D4×D53 | — | 4 | 2 | no | — |
| 179 | D4×D53 | — | 4 | 1 | no | — |
| 180 | D4×D53 | — | 4 | 1 | no | — |
| 181 | D4×D53 | — | 4 | 2 | no | — |
| 182 | #11719945 | — | 2 | 1 | no | — |
| 183 | #11719945 | — | 2 | 2 | no | — |
| 184 | #11719945 | — | 4 | 2 | no | — |
| 185 | #11719945 | — | 4 | 1 | no | — |
| 186 | #11719945 | — | 4 | 1 | no | — |
| 187 | #11719945 | — | 4 | 2 | no | — |
| 188 | C2×D212 | — | 2 | 1 | no | — |
| 189 | C2×D212 | — | 2 | 2 | no | — |
| 190 | C2×D212 | — | 2 | 2 | no | — |
| 191 | C2×D212 | — | 2 | 2 | no | — |
| 192 | C2×D212 | — | 4 | 1 | no | — |
| 193 | C2×D212 | — | 4 | 2 | no | — |
| 194 | C2×D212 | C2×D4 | 1 | 2 | yes | — |
| 195 | C2×D212 | C2×D4 | 1 | 2 | yes | — |
| 196 | C2×D212 | C2×D4 | 1 | 1 | yes | characteristic |
| 197 | C2×C4×D53 | — | 2 | 2 | no | — |
| 198 | C2×C4×D53 | — | 2 | 2 | no | — |
| 199 | C2×C4×D53 | — | 2 | 1 | no | — |
| 200 | C2×C4×D53 | — | 2 | 2 | no | — |
| 201 | C2×C4×D53 | — | 4 | 1 | no | — |
| 202 | C2×C4×D53 | — | 4 | 2 | no | — |
| 203 | C2×C4×D53 | — | 8 | 1 | no | — |
| 204 | C2×C4×D53 | — | 8 | 1 | no | — |
| 205 | C2×C4×D53 | C2×D4 | 1 | 2 | yes | — |
| 206 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 207 | C2×Dic106 | — | 2 | 1 | no | — |
| 208 | C2×Dic106 | C2×D4 | 1 | 1 | yes | characteristic |
| 209 | Q16×C53 | — | 4 | 2 | no | — |
| 210 | SD16×C53 | — | 4 | 2 | no | — |
| 211 | SD16×C53 | — | 4 | 1 | no | — |
| 212 | D8×C53 | — | 4 | 1 | no | — |
| 213 | M16×C53 | — | 2 | 1 | no | — |
| 214 | M16×C53 | — | 2 | 2 | no | — |
| 215 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 216 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 217 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 218 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 219 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 220 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 221 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 222 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 223 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 224 | C42×C53 | C2×D4 | 1 | 2 | yes | — |
| 225 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 226 | #11719925 | — | 4 | 2 | no | — |
| 227 | #11719925 | — | 4 | 1 | no | — |
| 228 | #11719924 | — | 4 | 2 | no | — |
| 229 | #11719924 | — | 4 | 2 | no | — |
| 230 | #11719923 | — | 4 | 1 | no | — |
| 231 | #11719923 | — | 4 | 1 | no | — |
| 232 | #11719922 | — | 4 | 1 | no | — |
| 233 | #11719922 | — | 4 | 2 | no | — |
| 234 | #11719921 | — | 2 | 2 | no | — |
| 235 | #11719921 | — | 2 | 2 | no | — |
| 236 | #11719921 | — | 2 | 2 | no | — |
| 237 | #11719921 | — | 2 | 2 | no | — |
| 238 | #11719921 | — | 2 | 2 | no | — |
| 239 | #11719921 | — | 2 | 2 | no | — |
| 240 | #11719921 | — | 2 | 2 | no | — |
| 241 | #11719921 | — | 2 | 2 | no | — |
| 242 | #11719921 | — | 2 | 2 | no | — |
| 243 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 244 | #11719919 | — | 2 | 2 | no | — |
| 245 | #11719919 | — | 2 | 2 | no | — |
| 246 | #11719919 | — | 2 | 2 | no | — |
| 247 | #11719919 | — | 2 | 2 | no | — |
| 248 | C4×Dic53 | — | 2 | 2 | no | — |
| 249 | C4×Dic53 | — | 2 | 1 | no | — |
| 250 | C4×Dic53 | C2×D4 | 1 | 2 | yes | — |
| 251 | C4×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 252 | #11719917 | — | 2 | 2 | no | — |
| 253 | #11719917 | — | 2 | 1 | no | — |
| 254 | Dic212 | — | 4 | 1 | no | — |
| 255 | D424 | — | 4 | 2 | no | — |
| 256 | #11719913 | — | 4 | 2 | no | — |
| 257 | #11719913 | — | 4 | 1 | no | — |
| 258 | #11719912 | — | 4 | 1 | no | — |
| 259 | #11719912 | — | 4 | 2 | no | — |
| 260 | C8×D53 | — | 4 | 1 | no | — |
| 261 | C8×D53 | — | 4 | 2 | no | — |
| 262 | C23×C53 | — | 2 | 1 | no | — |
| 263 | C22×D53 | — | 2 | 2 | no | — |
| 264 | C22×D53 | — | 4 | 2 | no | — |
| 265 | C22×D53 | — | 4 | 1 | no | — |
| 266 | C22×D53 | — | 8 | 1 | no | — |
| 267 | C22×D53 | — | 8 | 2 | no | — |
| 268 | C22×D53 | #120 | 1 | 2 | yes | — |
| 269 | C22×D53 | #120 | 1 | 1 | yes | characteristic |
| 270 | Q8×C53 | — | 2 | 2 | no | — |
| 271 | Q8×C53 | — | 2 | 1 | no | — |
| 272 | Q8×C53 | — | 4 | 1 | no | — |
| 273 | Q8×C53 | — | 4 | 2 | no | — |
| 274 | D4×C53 | — | 2 | 2 | no | — |
| 275 | D4×C53 | — | 2 | 1 | no | — |
| 276 | D4×C53 | — | 4 | 1 | no | — |
| 277 | D4×C53 | — | 4 | 1 | no | — |
| 278 | C2×C4×C53 | — | 2 | 1 | no | — |
| 279 | C2×C4×C53 | — | 2 | 2 | no | — |
| 280 | C2×C4×C53 | — | 2 | 2 | no | — |
| 281 | C2×C4×C53 | — | 4 | 1 | no | — |
| 282 | C2×C4×C53 | — | 4 | 2 | no | — |
| 283 | C2×C4×C53 | — | 8 | 1 | no | — |
| 284 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 285 | C2×C4×C53 | C22×D4 | 1 | 2 | yes | — |
| 286 | C22⋊D53 | — | 4 | 2 | no | — |
| 287 | C22⋊D53 | — | 4 | 1 | no | — |
| 288 | C22⋊D53 | — | 4 | 1 | no | — |
| 289 | C22⋊D53 | — | 4 | 1 | no | — |
| 290 | C22⋊D53 | — | 8 | 1 | no | — |
| 291 | C22⋊D53 | — | 8 | 2 | no | — |
| 292 | C22⋊D53 | — | 8 | 2 | no | — |
| 293 | C2×Dic53 | — | 2 | 2 | no | — |
| 294 | C2×Dic53 | — | 2 | 1 | no | — |
| 295 | C2×Dic53 | — | 2 | 1 | no | — |
| 296 | C2×Dic53 | — | 4 | 1 | no | — |
| 297 | C2×Dic53 | — | 4 | 1 | no | — |
| 298 | C2×Dic53 | — | 4 | 1 | no | — |
| 299 | C2×Dic53 | #120 | 1 | 1 | yes | characteristic |
| 300 | D212 | — | 2 | 1 | no | — |
| 301 | D212 | — | 2 | 2 | no | — |
| 302 | D212 | — | 4 | 1 | no | — |
| 303 | D212 | — | 4 | 2 | no | — |
| 304 | D212 | — | 4 | 2 | no | — |
| 305 | D212 | — | 4 | 2 | no | — |
| 306 | D212 | — | 4 | 1 | no | — |
| 307 | D212 | — | 8 | 2 | no | — |
| 308 | D212 | — | 8 | 1 | no | — |
| 309 | D212 | — | 8 | 2 | no | — |
| 310 | D212 | — | 8 | 2 | no | — |
| 311 | C4×D53 | — | 2 | 1 | no | — |
| 312 | C4×D53 | — | 2 | 2 | no | — |
| 313 | C4×D53 | — | 2 | 1 | no | — |
| 314 | C4×D53 | — | 2 | 2 | no | — |
| 315 | C4×D53 | — | 4 | 1 | no | — |
| 316 | C4×D53 | — | 4 | 2 | no | — |
| 317 | C4×D53 | — | 4 | 2 | no | — |
| 318 | C4×D53 | — | 4 | 1 | no | — |
| 319 | C4×D53 | — | 4 | 2 | no | — |
| 320 | C4×D53 | — | 4 | 2 | no | — |
| 321 | C4×D53 | — | 4 | 1 | no | — |
| 322 | C4×D53 | — | 8 | 2 | no | — |
| 323 | C4×D53 | — | 8 | 1 | no | — |
| 324 | C4×D53 | — | 8 | 2 | no | — |
| 325 | Dic106 | — | 2 | 2 | no | — |
| 326 | Dic106 | — | 2 | 1 | no | — |
| 327 | Dic106 | — | 4 | 1 | no | — |
| 328 | Dic106 | — | 4 | 1 | no | — |
| 329 | Dic106 | — | 8 | 1 | no | — |
| 330 | C8×C53 | — | 4 | 2 | no | — |
| 331 | C8×C53 | — | 4 | 1 | no | — |
| 332 | #88322 | — | 4 | 1 | no | — |
| 333 | #88322 | — | 4 | 2 | no | — |
| 334 | #33564 | — | 53 | 1 | no | maximal, Sylow |
| 335 | C22×C53 | — | 4 | 2 | no | — |
| 336 | C22×C53 | — | 4 | 1 | no | — |
| 337 | C22×C53 | — | 4 | 1 | no | — |
| 338 | C22×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 339 | C2×D53 | — | 2 | 2 | no | — |
| 340 | C2×D53 | — | 2 | 1 | no | — |
| 341 | C2×D53 | — | 4 | 1 | no | — |
| 342 | C2×D53 | — | 4 | 2 | no | — |
| 343 | C2×D53 | — | 4 | 2 | no | — |
| 344 | C2×D53 | — | 4 | 2 | no | — |
| 345 | C2×D53 | — | 4 | 1 | no | — |
| 346 | C2×D53 | — | 4 | 2 | no | — |
| 347 | C2×D53 | — | 8 | 4 | no | — |
| 348 | C2×D53 | — | 16 | 2 | no | — |
| 349 | C2×D53 | — | 16 | 1 | no | — |
| 350 | C4×C53 | — | 2 | 1 | no | — |
| 351 | C4×C53 | — | 2 | 2 | no | — |
| 352 | C4×C53 | — | 4 | 1 | no | — |
| 353 | C4×C53 | — | 4 | 2 | no | — |
| 354 | C4×C53 | — | 4 | 1 | no | — |
| 355 | C4×C53 | — | 4 | 2 | no | — |
| 356 | Dic53 | — | 4 | 2 | no | — |
| 357 | Dic53 | — | 4 | 1 | no | — |
| 358 | Dic53 | — | 4 | 1 | no | — |
| 359 | Dic53 | — | 4 | 1 | no | — |
| 360 | Dic53 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 361 | Dic53 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 362 | #3529 | — | 53 | 1 | no | — |
| 363 | #3018 | — | 53 | 2 | no | — |
| 364 | #3018 | — | 53 | 1 | no | — |
| 365 | #2203 | — | 53 | 2 | no | — |
| 366 | #2203 | — | 53 | 2 | no | — |
| 367 | #2203 | — | 53 | 1 | no | — |
| 368 | #2203 | D53 | 1 | 1 | yes | characteristic, complemented |
| 369 | #2202 | — | 53 | 1 | no | — |
| 370 | #2202 | — | 53 | 1 | no | — |
| 371 | #2132 | — | 53 | 2 | no | — |
| 372 | #2132 | — | 53 | 1 | no | — |
| 373 | C2×C53 | — | 2 | 1 | no | — |
| 374 | C2×C53 | — | 8 | 1 | no | — |
| 375 | C2×C53 | — | 8 | 1 | no | — |
| 376 | C2×C53 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 377 | D53 | — | 4 | 2 | no | — |
| 378 | D53 | — | 4 | 1 | no | — |
| 379 | D53 | — | 8 | 2 | no | — |
| 380 | D53 | — | 8 | 1 | no | — |
| 381 | #585 | — | 53 | 1 | no | — |
| 382 | #575 | — | 106 | 1 | no | — |
| 383 | #575 | — | 106 | 2 | no | — |
| 384 | #563 | — | 53 | 2 | no | — |
| 385 | #563 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 386 | #562 | — | 106 | 2 | no | — |
| 387 | #562 | — | 106 | 1 | no | — |
| 388 | H(3,𝔽4) | — | 53 | 1 | no | — |
| 389 | #560 | — | 106 | 1 | no | — |
| 390 | #560 | — | 106 | 2 | no | — |
| 391 | #532 | — | 53 | 2 | no | — |
| 392 | #532 | — | 53 | 1 | no | — |
| 393 | #529 | — | 106 | 1 | no | — |
| 394 | #529 | — | 106 | 2 | no | — |
| 395 | #525 | — | 106 | 2 | no | — |
| 396 | #525 | — | 106 | 1 | no | — |
| 397 | #456 | — | 53 | 1 | no | — |
| 398 | #456 | — | 53 | 2 | no | — |
| 399 | #456 | — | 53 | 1 | no | — |
| 400 | #456 | C2×D53 | 1 | 2 | yes | complemented |
| 401 | #455 | — | 106 | 1 | no | — |
| 402 | #455 | — | 106 | 2 | no | — |
| 403 | #454 | — | 53 | 2 | no | — |
| 404 | #454 | — | 53 | 1 | no | — |
| 405 | #454 | — | 53 | 2 | no | — |
| 406 | #454 | C2×D53 | 1 | 1 | yes | characteristic |
| 407 | #453 | — | 106 | 2 | no | — |
| 408 | #453 | — | 106 | 1 | no | — |
| 409 | C2×#104 | — | 106 | 2 | no | — |
| 410 | C2×#104 | — | 106 | 1 | no | — |
| 411 | #413 | — | 53 | 1 | no | — |
| 412 | #413 | — | 53 | 2 | no | — |
| 413 | #356 | — | 53 | 2 | no | — |
| 414 | #356 | — | 53 | 2 | no | — |
| 415 | #356 | C2×D53 | 1 | 2 | yes | complemented |
| 416 | #355 | — | 53 | 1 | no | — |
| 417 | #355 | — | 53 | 2 | no | — |
| 418 | #355 | — | 53 | 2 | no | — |
| 419 | #355 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 420 | C53 | #33564 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 421 | 2−1+4 | — | 53 | 1 | no | — |
| 422 | 2−1+4 | — | 212 | 1 | no | — |
| 423 | 2−1+4 | C22×D53 | 1 | 1 | yes | characteristic |
| 424 | H(5,𝔽2) | — | 106 | 1 | no | — |
| 425 | H(5,𝔽2) | — | 106 | 2 | no | — |
| 426 | H(5,𝔽2) | — | 212 | 1 | no | — |
| 427 | C2×#41 | — | 53 | 1 | no | — |
| 428 | C2×#41 | — | 53 | 2 | no | — |
| 429 | C2×#41 | — | 53 | 1 | no | — |
| 430 | C2×#41 | — | 106 | 1 | no | — |
| 431 | C2×#41 | — | 106 | 2 | no | — |
| 432 | C2×#41 | — | 212 | 1 | no | — |
| 433 | C2×#41 | — | 212 | 1 | no | — |
| 434 | C23×C4 | — | 106 | 1 | no | — |
| 435 | #137 | — | 2 | 2 | no | — |
| 436 | #137 | — | 106 | 1 | no | — |
| 437 | #137 | — | 106 | 1 | no | — |
| 438 | #137 | — | 106 | 2 | no | — |
| 439 | #137 | — | 212 | 1 | no | — |
| 440 | #137 | — | 212 | 2 | no | — |
| 441 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 442 | AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 443 | AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 444 | AGL(1,ℤ/8) | — | 106 | 1 | no | — |
| 445 | AGL(1,ℤ/8) | — | 212 | 1 | no | — |
| 446 | AGL(1,ℤ/8) | — | 212 | 2 | no | — |
| 447 | #135 | — | 212 | 1 | no | — |
| 448 | #135 | — | 212 | 2 | no | — |
| 449 | #135 | — | 212 | 1 | no | — |
| 450 | #135 | — | 212 | 2 | no | — |
| 451 | C2×M16 | — | 106 | 1 | no | — |
| 452 | C2×M16 | — | 106 | 2 | no | — |
| 453 | C4⋊Q8 | — | 53 | 1 | no | — |
| 454 | C4⋊Q8 | C22×D53 | 1 | 2 | yes | — |
| 455 | #127 | — | 53 | 1 | no | — |
| 456 | #127 | — | 53 | 2 | no | — |
| 457 | #126 | — | 2 | 2 | no | — |
| 458 | #126 | — | 106 | 2 | no | — |
| 459 | #126 | — | 106 | 2 | no | — |
| 460 | #125 | — | 2 | 1 | no | — |
| 461 | #125 | — | 106 | 2 | no | — |
| 462 | #124 | — | 53 | 2 | no | — |
| 463 | #124 | — | 53 | 2 | no | — |
| 464 | #124 | — | 53 | 1 | no | — |
| 465 | #124 | — | 106 | 2 | no | — |
| 466 | #124 | — | 106 | 1 | no | — |
| 467 | #124 | C22×D53 | 1 | 1 | yes | characteristic |
| 468 | #123 | — | 2 | 1 | no | — |
| 469 | #123 | — | 106 | 2 | no | — |
| 470 | #123 | — | 106 | 2 | no | — |
| 471 | #123 | — | 106 | 2 | no | — |
| 472 | #123 | — | 106 | 2 | no | — |
| 473 | #123 | — | 106 | 2 | no | — |
| 474 | #123 | — | 106 | 1 | no | — |
| 475 | C22⋊Q8 | — | 2 | 2 | no | — |
| 476 | C22⋊Q8 | — | 106 | 2 | no | — |
| 477 | C22⋊Q8 | — | 106 | 2 | no | — |
| 478 | C22⋊Q8 | — | 106 | 1 | no | — |
| 479 | C22⋊Q8 | — | 106 | 2 | no | — |
| 480 | #121 | — | 106 | 2 | no | — |
| 481 | #121 | — | 106 | 2 | no | — |
| 482 | #121 | — | 106 | 2 | no | — |
| 483 | #121 | — | 106 | 2 | no | — |
| 484 | #121 | — | 106 | 2 | no | — |
| 485 | #121 | — | 106 | 2 | no | — |
| 486 | #121 | — | 106 | 1 | no | — |
| 487 | #121 | — | 106 | 2 | no | — |
| 488 | #120 | — | 106 | 2 | no | — |
| 489 | #120 | — | 106 | 1 | no | — |
| 490 | #120 | — | 106 | 2 | no | — |
| 491 | #120 | — | 106 | 1 | no | — |
| 492 | C4×Q8 | — | 106 | 1 | no | — |
| 493 | C4×D4 | — | 106 | 2 | no | — |
| 494 | C4×D4 | — | 106 | 2 | no | — |
| 495 | C4×D4 | — | 106 | 2 | no | — |
| 496 | C4×D4 | — | 106 | 2 | no | — |
| 497 | C4×D4 | — | 106 | 1 | no | — |
| 498 | #117 | — | 106 | 1 | no | — |
| 499 | #117 | — | 106 | 2 | no | — |
| 500 | C2×C42 | — | 53 | 2 | no | — |
| 501 | C2×C42 | — | 53 | 1 | no | — |
| 502 | #104 | — | 2 | 2 | no | — |
| 503 | #104 | — | 2 | 1 | no | — |
| 504 | #104 | — | 106 | 1 | no | — |
| 505 | #104 | — | 106 | 2 | no | — |
| 506 | #104 | — | 106 | 1 | no | — |
| 507 | #104 | — | 106 | 2 | no | — |
| 508 | #104 | — | 106 | 2 | no | — |
| 509 | #104 | — | 106 | 1 | no | — |
| 510 | #101 | — | 53 | 1 | no | — |
| 511 | #101 | — | 53 | 2 | no | — |
| 512 | #101 | C22×D53 | 1 | 1 | yes | characteristic |
| 513 | #101 | C22×D53 | 1 | 2 | yes | — |
| 514 | #100 | — | 106 | 1 | no | — |
| 515 | #100 | — | 106 | 2 | no | — |
| 516 | C24 | — | 106 | 1 | no | — |
| 517 | #41 | — | 2 | 1 | no | — |
| 518 | #41 | — | 2 | 2 | no | — |
| 519 | #41 | — | 4 | 1 | no | — |
| 520 | #41 | — | 106 | 1 | no | — |
| 521 | #41 | — | 106 | 2 | no | — |
| 522 | #41 | — | 106 | 1 | no | — |
| 523 | #41 | — | 106 | 2 | no | — |
| 524 | #41 | — | 106 | 2 | no | — |
| 525 | #41 | — | 106 | 1 | no | — |
| 526 | #41 | — | 212 | 1 | no | — |
| 527 | #41 | — | 212 | 2 | no | — |
| 528 | #41 | — | 212 | 1 | no | — |
| 529 | #41 | — | 212 | 2 | no | — |
| 530 | #41 | — | 212 | 1 | no | — |
| 531 | #41 | — | 212 | 1 | no | — |
| 532 | #41 | — | 212 | 1 | no | — |
| 533 | #41 | — | 212 | 1 | no | — |
| 534 | #41 | — | 212 | 1 | no | — |
| 535 | #41 | — | 212 | 2 | no | — |
| 536 | #41 | — | 212 | 2 | no | — |
| 537 | #41 | — | 212 | 1 | no | — |
| 538 | #41 | — | 212 | 1 | no | — |
| 539 | #41 | — | 212 | 2 | no | — |
| 540 | C2×Q8 | — | 4 | 1 | no | — |
| 541 | C2×Q8 | — | 53 | 1 | no | — |
| 542 | C2×Q8 | — | 106 | 1 | no | — |
| 543 | C2×Q8 | — | 106 | 1 | no | — |
| 544 | C2×Q8 | — | 106 | 2 | no | — |
| 545 | C2×Q8 | — | 212 | 1 | no | — |
| 546 | C2×Q8 | D4×D53 | 1 | 2 | yes | — |
| 547 | C2×Q8 | C23×D53 | 1 | 1 | yes | characteristic |
| 548 | C2×D4 | — | 53 | 2 | no | — |
| 549 | C2×D4 | — | 53 | 1 | no | — |
| 550 | C2×D4 | — | 53 | 2 | no | — |
| 551 | C2×D4 | — | 106 | 2 | no | — |
| 552 | C2×D4 | — | 106 | 2 | no | — |
| 553 | C2×D4 | — | 106 | 2 | no | — |
| 554 | C2×D4 | — | 106 | 1 | no | — |
| 555 | C2×D4 | — | 106 | 1 | no | — |
| 556 | C2×D4 | — | 106 | 2 | no | — |
| 557 | C2×D4 | — | 106 | 2 | no | — |
| 558 | C2×D4 | — | 106 | 1 | no | — |
| 559 | C2×D4 | — | 106 | 2 | no | — |
| 560 | C2×D4 | — | 212 | 1 | no | — |
| 561 | C2×D4 | — | 212 | 2 | no | — |
| 562 | C2×D4 | — | 212 | 1 | no | — |
| 563 | C2×D4 | — | 212 | 2 | no | — |
| 564 | C2×D4 | — | 212 | 1 | no | — |
| 565 | C2×D4 | — | 212 | 2 | no | — |
| 566 | C2×D4 | D4×D53 | 1 | 1 | yes | characteristic |
| 567 | C22×C4 | — | 2 | 1 | no | — |
| 568 | C22×C4 | — | 53 | 2 | no | — |
| 569 | C22×C4 | — | 53 | 1 | no | — |
| 570 | C22×C4 | — | 106 | 2 | no | — |
| 571 | C22×C4 | — | 106 | 1 | no | — |
| 572 | C22×C4 | — | 106 | 2 | no | — |
| 573 | C22×C4 | — | 106 | 2 | no | — |
| 574 | C22×C4 | — | 106 | 1 | no | — |
| 575 | C22×C4 | — | 424 | 1 | no | — |
| 576 | C22×C4 | — | 424 | 1 | no | — |
| 577 | C22×C4 | — | 212 | 1 | no | — |
| 578 | C22×C4 | — | 212 | 2 | no | — |
| 579 | Q16 | — | 4 | 2 | no | — |
| 580 | Q16 | — | 212 | 1 | no | — |
| 581 | Q16 | — | 212 | 1 | no | — |
| 582 | Q16 | — | 212 | 2 | no | — |
| 583 | SD16 | — | 4 | 2 | no | — |
| 584 | SD16 | — | 4 | 1 | no | — |
| 585 | SD16 | — | 212 | 1 | no | — |
| 586 | SD16 | — | 212 | 2 | no | — |
| 587 | SD16 | — | 212 | 1 | no | — |
| 588 | SD16 | — | 212 | 1 | no | — |
| 589 | SD16 | — | 212 | 2 | no | — |
| 590 | SD16 | — | 212 | 2 | no | — |
| 591 | D8 | — | 4 | 1 | no | — |
| 592 | D8 | — | 212 | 2 | no | — |
| 593 | D8 | — | 212 | 2 | no | — |
| 594 | D8 | — | 212 | 1 | no | — |
| 595 | M16 | — | 2 | 1 | no | — |
| 596 | M16 | — | 2 | 2 | no | — |
| 597 | M16 | — | 106 | 2 | no | — |
| 598 | M16 | — | 106 | 1 | no | — |
| 599 | M16 | — | 212 | 1 | no | — |
| 600 | M16 | — | 212 | 2 | no | — |
| 601 | C2×C8 | — | 212 | 1 | no | — |
| 602 | C2×C8 | — | 212 | 2 | no | — |
| 603 | C4⋊C4 | — | 2 | 2 | no | — |
| 604 | C4⋊C4 | — | 2 | 1 | no | — |
| 605 | C4⋊C4 | — | 2 | 1 | no | — |
| 606 | C4⋊C4 | — | 2 | 2 | no | — |
| 607 | C4⋊C4 | — | 2 | 2 | no | — |
| 608 | C4⋊C4 | — | 106 | 2 | no | — |
| 609 | C4⋊C4 | — | 106 | 2 | no | — |
| 610 | C4⋊C4 | — | 106 | 2 | no | — |
| 611 | C4⋊C4 | — | 106 | 2 | no | — |
| 612 | C4⋊C4 | — | 106 | 2 | no | — |
| 613 | C22⋊C4 | — | 2 | 1 | no | — |
| 614 | C22⋊C4 | — | 2 | 2 | no | — |
| 615 | C22⋊C4 | — | 2 | 2 | no | — |
| 616 | C22⋊C4 | — | 106 | 2 | no | — |
| 617 | C22⋊C4 | — | 106 | 2 | no | — |
| 618 | C22⋊C4 | — | 106 | 2 | no | — |
| 619 | C22⋊C4 | — | 106 | 2 | no | — |
| 620 | C22⋊C4 | — | 106 | 2 | no | — |
| 621 | C22⋊C4 | — | 106 | 2 | no | — |
| 622 | C22⋊C4 | — | 106 | 2 | no | — |
| 623 | C22⋊C4 | — | 106 | 1 | no | — |
| 624 | C22⋊C4 | — | 106 | 2 | no | — |
| 625 | C22⋊C4 | — | 106 | 2 | no | — |
| 626 | C42 | — | 53 | 2 | no | — |
| 627 | C42 | — | 53 | 1 | no | — |
| 628 | C42 | — | 106 | 1 | no | — |
| 629 | C42 | — | 106 | 2 | no | — |
| 630 | C42 | D4×D53 | 1 | 1 | yes | characteristic |
| 631 | C42 | D4×D53 | 1 | 2 | yes | — |
| 632 | C23 | — | 2 | 1 | no | — |
| 633 | C23 | — | 53 | 1 | no | — |
| 634 | C23 | — | 53 | 2 | no | — |
| 635 | C23 | — | 106 | 2 | no | — |
| 636 | C23 | — | 424 | 1 | no | — |
| 637 | C23 | — | 424 | 2 | no | — |
| 638 | C23 | — | 212 | 2 | no | — |
| 639 | C23 | — | 212 | 1 | no | — |
| 640 | Q8 | — | 2 | 1 | no | — |
| 641 | Q8 | — | 2 | 2 | no | — |
| 642 | Q8 | — | 4 | 1 | no | — |
| 643 | Q8 | — | 4 | 2 | no | — |
| 644 | Q8 | — | 106 | 1 | no | — |
| 645 | Q8 | — | 106 | 2 | no | — |
| 646 | Q8 | — | 424 | 1 | no | — |
| 647 | Q8 | — | 212 | 1 | no | — |
| 648 | Q8 | — | 212 | 1 | no | — |
| 649 | D4 | — | 2 | 1 | no | — |
| 650 | D4 | — | 2 | 2 | no | — |
| 651 | D4 | — | 4 | 1 | no | — |
| 652 | D4 | — | 4 | 1 | no | — |
| 653 | D4 | — | 106 | 1 | no | — |
| 654 | D4 | — | 106 | 2 | no | — |
| 655 | D4 | — | 424 | 2 | no | — |
| 656 | D4 | — | 424 | 2 | no | — |
| 657 | D4 | — | 424 | 2 | no | — |
| 658 | D4 | — | 424 | 1 | no | — |
| 659 | D4 | — | 424 | 1 | no | — |
| 660 | D4 | — | 424 | 2 | no | — |
| 661 | D4 | — | 424 | 2 | no | — |
| 662 | D4 | — | 212 | 1 | no | — |
| 663 | D4 | — | 212 | 2 | no | — |
| 664 | D4 | — | 212 | 2 | no | — |
| 665 | D4 | — | 212 | 2 | no | — |
| 666 | D4 | — | 212 | 1 | no | — |
| 667 | D4 | — | 212 | 1 | no | — |
| 668 | D4 | — | 212 | 2 | no | — |
| 669 | D4 | — | 212 | 1 | no | — |
| 670 | D4 | — | 212 | 1 | no | — |
| 671 | C2×C4 | — | 2 | 1 | no | — |
| 672 | C2×C4 | — | 2 | 2 | no | — |
| 673 | C2×C4 | — | 2 | 2 | no | — |
| 674 | C2×C4 | — | 4 | 1 | no | — |
| 675 | C2×C4 | — | 4 | 2 | no | — |
| 676 | C2×C4 | — | 8 | 1 | no | — |
| 677 | C2×C4 | — | 53 | 1 | no | — |
| 678 | C2×C4 | — | 106 | 1 | no | — |
| 679 | C2×C4 | — | 106 | 2 | no | — |
| 680 | C2×C4 | — | 106 | 1 | no | — |
| 681 | C2×C4 | — | 106 | 2 | no | — |
| 682 | C2×C4 | — | 106 | 2 | no | — |
| 683 | C2×C4 | — | 106 | 1 | no | — |
| 684 | C2×C4 | — | 106 | 1 | no | — |
| 685 | C2×C4 | — | 424 | 2 | no | — |
| 686 | C2×C4 | — | 424 | 1 | no | — |
| 687 | C2×C4 | — | 424 | 2 | no | — |
| 688 | C2×C4 | — | 212 | 1 | no | — |
| 689 | C2×C4 | — | 212 | 2 | no | — |
| 690 | C2×C4 | — | 212 | 2 | no | — |
| 691 | C2×C4 | — | 212 | 2 | no | — |
| 692 | C2×C4 | — | 212 | 1 | no | — |
| 693 | C2×C4 | — | 212 | 2 | no | — |
| 694 | C2×C4 | — | 212 | 1 | no | — |
| 695 | C2×C4 | — | 212 | 1 | no | — |
| 696 | C2×C4 | — | 212 | 1 | no | — |
| 697 | C2×C4 | — | 212 | 1 | no | — |
| 698 | C2×C4 | C2×D4×D53 | 1 | 2 | yes | — |
| 699 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 700 | C8 | — | 4 | 1 | no | — |
| 701 | C8 | — | 4 | 2 | no | — |
| 702 | C8 | — | 212 | 1 | no | — |
| 703 | C8 | — | 212 | 2 | no | — |
| 704 | C22 | — | 4 | 2 | no | — |
| 705 | C22 | — | 4 | 1 | no | — |
| 706 | C22 | — | 4 | 1 | no | — |
| 707 | C22 | — | 848 | 2 | no | — |
| 708 | C22 | — | 848 | 1 | no | — |
| 709 | C22 | — | 106 | 2 | no | — |
| 710 | C22 | — | 106 | 1 | no | — |
| 711 | C22 | — | 424 | 4 | no | — |
| 712 | C22 | — | 212 | 2 | no | — |
| 713 | C22 | — | 212 | 2 | no | — |
| 714 | C22 | — | 212 | 1 | no | — |
| 715 | C22 | — | 212 | 2 | no | — |
| 716 | C22 | — | 212 | 2 | no | — |
| 717 | C22 | — | 212 | 1 | no | — |
| 718 | C22 | #120×D53 | 1 | 1 | yes | characteristic |
| 719 | C4 | — | 2 | 1 | no | — |
| 720 | C4 | — | 2 | 2 | no | — |
| 721 | C4 | — | 4 | 2 | no | — |
| 722 | C4 | — | 4 | 1 | no | — |
| 723 | C4 | — | 4 | 2 | no | — |
| 724 | C4 | — | 4 | 1 | no | — |
| 725 | C4 | — | 53 | 1 | no | — |
| 726 | C4 | — | 53 | 1 | no | — |
| 727 | C4 | — | 212 | 1 | no | — |
| 728 | C4 | — | 212 | 2 | no | — |
| 729 | C4 | — | 212 | 1 | no | — |
| 730 | C4 | — | 212 | 1 | no | — |
| 731 | C2 | — | 2 | 1 | no | — |
| 732 | C2 | — | 8 | 1 | no | — |
| 733 | C2 | — | 8 | 1 | no | — |
| 734 | C2 | — | 424 | 1 | no | — |
| 735 | C2 | — | 424 | 2 | no | — |
| 736 | C2 | — | 212 | 2 | no | — |
| 737 | C2 | — | 212 | 1 | no | — |
| 738 | C2 | B(4,𝔽2)×D53 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20288856 | C2 | semidirect |
| 2. #20284067 | C2 | semidirect |
| 3. #20284062 | C2 | semidirect |
| 4. #20276737 | C2 | semidirect |
| 5. #20276736 | C2 | semidirect |
| 6. #20276734 | C2 | semidirect |
| 7. #20276733 | C2 | semidirect |
| 8. #20276731 | C2 | semidirect |
| 9. #20276399 | C2 | semidirect |
| 10. #20276397 | C2 | semidirect |
| 11. C53×#2203 | C2 | semidirect |
| 12. #16811460 | C22 | semidirect |
| 15. #16811372 | C22 | semidirect |
| 18. #16811365 | C22 | semidirect |
| 27. #16810808 | C22 | semidirect |
| 28. #16810806 | C22 | semidirect |
| 29. #16810805 | C22 | semidirect |
| 39. #16810606 | C22 | semidirect |
| 40. #16810606 | C22 | semidirect |
| 41. #16810422 | C22 | semidirect |
| 42. #16810421 | C22 | semidirect |
| 43. #16810420 | C22 | semidirect |
| 44. #16810419 | C22 | semidirect |
| 45. #16810419 | C22 | semidirect |
| 46. C53×#563 | C22 | semidirect |
| 47. C53×#456 | C22 | semidirect |
| 49. C53×#356 | C22 | semidirect |
| 50. C53×#355 | C22 | semidirect |
| 368. #2203 | D53 | semidirect |
| 385. #563 | C2×D53 | semidirect |
| 400. #456 | C2×D53 | semidirect |
| 415. #356 | C2×D53 | semidirect |
| 419. #355 | C2×D53 | semidirect |
| 420. C53 | #33564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288856 | 2 |
| #20284067 | 2 |
| #20284062 | 2 |
| #20276737 | 2 |
| #20276736 | 2 |
| #20276734 | 2 |
| #20276733 | 2 |
| #20276731 | 2 |
| #20276399 | 2 |
| #20276397 | 2 |
| C53×#2203 | 2 |
| #33564 | 53 |